Question

A shopkeeper fixes the selling price of his goods at 60% above the cost price. He sells half of his stock at this price, a quarter of his stock at a discount of 25% on the original selling price, and the rest at a discount of 50% on the original selling price. Find the gain percent altogether.

Answer 1

Let the C.P. of each article bought = Rs.100
Let the number of articles bought = x
∴ C.P. of the articles = Rs.100x
M.P. of the articles
= Rs.100 + 60% of Rs.100
= Rs.160
Stage 1 :
No. of articles sold at Rs.160 = `x/(2)`

∴ S.P. of `x/(2)`articles

= Rs.`(160 xx x/2)`
= Rs.80x
Stage 2 :
Discount
= 25% of Rs.160
= `(25)/(100) xx "Rs."160`
= Rs.40
∴ S.P. 
= Rs.160 - Rs.40
= Rs.120
No. of articles sold at Rs.120 = `x/(4)`

∴ S.P. of `x/(4)`articles

= Rs.`(120 xx x/4)`
= Rs.30x
Stage 3 :
Discount
= 50% of Rs.160
= `(50)/(100) xx "Rs."160`
= Rs.80
∴ S.P.
= Rs.160 - Rs.80
= Rs.80
No. of articles sold at Rs.80 = `x/(4)`

∴ S.P. of `x/(4)`articles

= Rs.`(80 xx x/4)`
= Rs.20x
Total S.P. of all articles
= Rs.80x + Rs.30x + Rs.20x
= Rs.130x
∵ S.P. > C.P., therefore there is a gain
Gain
= Rs.130x - Rs.100x
= Rs.30x
Gain %
= `"gain"/"C.P." xx 100`

= `(30x)/(100x) xx 100`
= 30%.